Generally for DX a takeoff angle of 30 degrees or less is the rule of
thumb for best general performance.
Of course the antenna still "works" at other heights, but if DX is what
you want to achieve, then best results, on the average over average
ground, the antenna will work best for that at a height of .5 lambda
or better.
Now is you happen to be in a salt water marsh surrounded by 100 foot
tall steel blimp hangers, your results may vary.
You ignore the fact this is an idealized environment. That is NEVER the
case in a real installation.
You ignore the fact this is modeled on an AVERAGE environment.
I have WAS on 75 SSB (from Iowa) with an inverted Vee. The top was only
50' in the air. And late at night in the wintertime I had pretty solid
communications over much of the continental U.S. (back in the late 70's
and early 80's).
Big whoop.
The post wasn't about how many QSL cards have been collected, it was
about antenna patterns.
Antennas NEVER work "as predicted" - and anyone who claims they do does
not understand antenna operation.
Any prediction is as good as the model used to make the prediction.
If one can not build a model that is accurate to about two digit accuracy,
then they shouldn't be trying to build models.